Electronic image data, such as data that creates a television image, must be processed in various ways to make it usable under different circumstances. For example, an image must be resized if it is to be displayed on a smaller screen than the screen for which it was originally formatted. Resizing involves the basic ideas of low-pass filtering, resampling, and decimation. Resampling a signal at a different rate is equivalent to converting a sampled signal to analog using a digital to analog converter (DAC), analog reconstruction filtering, and sampling at a new rate using an ADC, but a much better job can be done entirely in the digital domain.
The resample ratio (output pixels/input pixels) is always from one image to another. Typically, the source image to be resized is broken up into tiles, each of which is processed independently. The output image is re-formed from the tiles in such a way that the resulting picture is acceptable, and ideally no different from an image that had been processed as one large tile. For this precise behavior, the ratios can require as many bits to represent the numerator and denominator as would be needed to represent the largest image widths or heights.
To allow tiling, the top-left pixels of the source and destination images are chosen to be co-sited. A ratio between the images is determined such that one pixel beyond the right-most column of pixels in the source and destination images are also co-sited. The same applies vertically.
For an input sample rate of fsample down-sampled to a lower output sample rate fresample, any original sampled frequency components f near (but by definition, less than) the Nyquist limit fsample/2 may cause spectral aliasing.
                                          If            ⁢                                                  ⁢                          f              resample                                <                      f            sample                          ⁢                                  ⁢        and                            (                  EQ          ⁢                                          ⁢          1                )                                f        >                              f            sample                    2                                    (                  EQ          ⁢                                          ⁢          2                )            
then spectral aliasing occurs atfalias=fsample−f  (EQ 3)
A polyphase filter system can do these two operations (in the required order) in one filter system, to generate each output sample. However, the polyphase filter approach comes with a high hardware cost, as each filter coefficient set has to form a low-pass filter, and multiple sets of such filter coefficients are required to generate the resampled signal at different output phases. The number of phases used should reflect the target precision of the system, and is usually derived by quantizing results from the ratioing sub-system (which can be implemented exactly using integer arithmetic). Because a polyphase filter will be used only for resizing the majority of the time, the amount of hardware required may not be justified. For example, a two-dimensional (2-D) polyphase filter requires a very large 2-D filter array with a high gate count for good quality frequency response characteristics with acceptable frequency aliasing. The 2-D polyphase filter also requires a large amount of random access memory (RAM) on each filter tap, and a high 2-D read access bandwidth into the polyphase filter. The high bandwidth requires a large amount of register file image storage rather than RAM.
One-dimensional (1-D) polyphase filters can be used for both limited low-pass filtering and resampling in the same pass, but they also require a relatively large number of gates. Another disadvantage is the relative complexity of designing the polyphase coefficients for each application. Even if only used for resizing, the new low-pass filtering characteristics have to be re-calculated for all the resampling phases. This makes dynamic resizing software for the 1-D polyphase filter much slower and less responsive to the user.